An explicit height bound for the classical modular polynomial
Number Theory
2012-06-26 v2
Abstract
For a prime m, let Phi_m be the classical modular polynomial, and let h(Phi_m) denote its logarithmic height. By specializing a theorem of Cohen, we prove that h(Phi_m) <= 6 m log m + 16 m + 14 sqrt m log m. As a corollary, we find that h(Phi_m) <= 6 m log m + 18 m also holds. A table of h(Phi_m) values is provided for m <= 3607.
Cite
@article{arxiv.0909.3442,
title = {An explicit height bound for the classical modular polynomial},
author = {Reinier Broker and Andrew V. Sutherland},
journal= {arXiv preprint arXiv:0909.3442},
year = {2012}
}
Comments
Minor correction to the constants in Theorem 1 and Corollary 9. To appear in the Ramanujan Journal. 17 pages.